A number written in decimal form can terminate (or repeat) long after the last digit that you know.
So, knowing a few digits (even a hundred digits!) may not be enough.
If the decimal represents a root, such as the square root or cube root or fourth root (etc), then you can tell if the number is rational or irrational depending upon whether the decimal represents a perfect square, cube, fourth (etc.).
For instance, if the decimal is 0.10251663... and if it turns out to be 0.1025166375025 000000... it is a perfect square and has a square root of 0.1012505.
If the number is like this: 0.10110111011110111110... it has a pattern that doesn't repeat, so it's an irrational number.